Formal System (Partial) BibliographyFormal System (Partial) Bibliography
This note lists some works that discuss formal systems or exhibit formal systems (especially in the arts). Some are quite specialized, bu...
I gave a talk entitled Creativity and Constraint – Queering the Formal System to a small virtual gathering of friends in November of 2020. For many years prior, (since about 2012), I had been fascinated by the concept of formal systemsFormal System
What is a formal system?
Start with an [[Axiom]]
Continue with a rule or self-imposed constraintFormal Constraint
Quick Definition
Mathematics
A formal constraint (what I consider to be analogous with [[Gödel, Escher, Bach- An Eternal Golden Braid|Hofstadter's]] "rule of production" or "rule of inference") is a method for transforming one result of a formal system into another result. In mathematics, we can use mathematical induction to derive a theorem from an axiom or from another theorem. Because we trust that our rules of induction will preserve the truth of our mathematical statements, following t...
Apply the rules and constraints to the axiom and see what happens!
This definition is loosely based on Hofstadter’s [[Gödel, Escher, Bach- An Eternal Golden Braid]] (GEB) and on my own experience making and breaking formal systems.
Start with an axiom (in mathematics) or idea/material (creative disciplines like the arts).
A rule or constraint develops ..., where a thinker, writer, musician, mathematician, etc. uses a set of rules to create something new from some initial ideas or "materials." Note that this is an extreme simplification of this concept for the purpose of introducing a much larger discussion.
I applied this concept of formal systems to the way that I compose music, developing a strong interest in how form and musical materials relate to one another, and eventually becoming fascinated by the use of constraintsFormal Constraint
Quick Definition
Mathematics
A formal constraint (what I consider to be analogous with [[Gödel, Escher, Bach- An Eternal Golden Braid|Hofstadter's]] "rule of production" or "rule of inference") is a method for transforming one result of a formal system into another result. In mathematics, we can use mathematical induction to derive a theorem from an axiom or from another theorem. Because we trust that our rules of induction will preserve the truth of our mathematical statements, following t... in the music of other composers, in literatureOulipo
A Workshop of Potential Literature
The Oulipo or "Workshop of Potential Literature" was a French literary movement inspired by Dadaism, absurdism, and the 'Pataphysics movement. The writers who comprised the Oulipo focused their work on exploring the role that [[Formal Constraint|constraints]] could play in creating new works.
Perec's A Void
The most prominent Oulipian figure, Georges PerecPerec, Georges
Georges Perec was a French author and thinker and a member of the [[Oulipo]] literary group. He is best known for his various books: W, or Memories of Childhood, [[A Void]], and [[Life a User’s Manual]].
Perec's works reflect his interest in constraint techniques, chance, fate, determinism, and memory. See more in the note on the [[Oulipo]].
Resources
James, Alison. Constraining Chance: Georges Perec and the Oulipo. Evanston, IL: Northwestern University Press, 2009.
Last modified on ..., gives a numbers of excellent examples of these constraint techniques at play. His..., and in techniques such as computer-assisted composition.
During this time I began to realize that I was attracted to other men. I was part of a Christian culture that failed to provide a hopeful vocation for LGBTQ+ believers, and so I began to repress my experience as best I could. As I continued through college and the beginning of grad school, I increasingly felt this constant, oppressive sense of failure, otherness, and unwelcomeness in the church. I felt as though I was "disqualified" from participating in Christian communities, from being discipled, from engaging deeply with any element of my faith until I had "figured out" how to be straight. I didn't have language for this perspective at the time, but it is what is commonly referred to as a "side X" theological position. For further details, see the frequently-referenced article on the "sides" terminology from Aaron at the blog Strength of His Might.
Finally in 2019, I encountered the book A War of Loves by David Bennett. Bennett described his early life as a gay activist, his later embrace of Christianity, and the difficult journey of reconciling his sexuality and faith. This book referenced an entirely different theological perspective than what I had known– a position called "side B." This view calls LGBTQ+ Christians to pursue celibacy or opposite-sex marriage, embracing what some call a form of "costly obedience." Zaporozhets, Olya, and Mark A. Yarhouse. Costly Obedience: What We Can Learn from the Celibate Gay Christian Community. Grand Rapids: Zondervan Reflective, 2019.
The upshot of Bennett's story, as well as the stories of so many side B people, is that this way of life can lead to unique joy and purpose.
As I began to embrace this calling for my own life, I was naturally drawn to once again consider the ideas that had been so helpful before – formal systems, constraints, the surprising and the sublime. It felt quite natural that this new constraint in my life (choosing to be single and celibate) could be yet another example of the same principle with which I was so familiar– a self-imposed constraint can lead to transcendent, surprising, and entirely unique …one might even say queer…
outcomes.
This was the context in which I came to put together this brief 10-minute talk. There was no recording, and I didn't write out a full transcript of what I would say, but I'll give the general outline below:
What is a formal system?
A formal system is used for constructing an abstract thought or artistic work from a collection of axioms or materials according to a set of rules or constraints.*
*this is my own humanities-inclusive definition…
A formal system is an organized way of thinking that involves three components: axioms, constraints, and a result. I first became familiar with the concept of formal systems by reading Douglas Hofstadter's book, Gödel, Escher, Bach: An Eternal Golden BraidGödel, Escher, Bach- An Eternal Golden Braid
Purchase a copy on IndieBound.
Read the Wikipedia article on GEB.
Background
I first encountered this book by Douglas Hofstadter in high school and became enraptured. The concepts from Gödel, Escher, Bach that have most influenced my thinking and artistic practice are summarized in the notes to "Creativity and Constraint: Queering the Formal System."
Gödel, Escher, Bach (also abbreviated as GEB) usually proves too difficult for me to adequately summarize in conversation; I'll try to be.... Hofstadter explains how formal systems are related to the concepts of self-reference, paradox, logic, and the nature of artificial intelligence (among other ideas). Since reading Hofstadter's work, I have applied the framework of formal systems to a wide variety of subjects and situations apart from its original context (mathematics); I primarily use formal systems to conceptualize my work as a composer.
I'll briefly restate the components of a formal system:
- Start with an axiomAxiom
Quick Definition
An axiom is a logical presupposition that cannot be proven to be true – instead, we take it on faith that it is true.
Use in Mathematics
In mathematics, subjects like Geometry rely on a set of axioms that mathematicians "take on faith" in order to begin using mathematical induction to draw conclusions and develop more advanced theorems. Changing these axioms can lead to dramatically different results – for example, you can obtain spherical geometry and hyperbolic geometry ... (as in mathematics or logic) or a collection of material (as in music or the arts). - Continue with a rule or self-imposed constraintFormal Constraint
Quick Definition
Mathematics
A formal constraint (what I consider to be analogous with [[Gödel, Escher, Bach- An Eternal Golden Braid|Hofstadter's]] "rule of production" or "rule of inference") is a method for transforming one result of a formal system into another result. In mathematics, we can use mathematical induction to derive a theorem from an axiom or from another theorem. Because we trust that our rules of induction will preserve the truth of our mathematical statements, following t... (this could be something such as a logical "inference rule" or a musical "developmental technique"). - Finish with the result of the process (in mathematics this would be a theorem, in composition it is a completed piece of music).
Where do axioms come from?
It is important to note that axiomsAxiom
Quick Definition
An axiom is a logical presupposition that cannot be proven to be true – instead, we take it on faith that it is true.
Use in Mathematics
In mathematics, subjects like Geometry rely on a set of axioms that mathematicians "take on faith" in order to begin using mathematical induction to draw conclusions and develop more advanced theorems. Changing these axioms can lead to dramatically different results – for example, you can obtain spherical geometry and hyperbolic geometry ... (or the germ that a composer might use as their primary musical material) seems to have their own independent sort of existence. Axioms are typically described as true statements that cannot be proven – to take an example from mathematics, the concept that all 90º angles are equivalent to one another is simply taken on faith. Geometers will assume that this is true and continue the course of their logical reasoning without actually proving that this statement is true.
In what I consider to be an analogous situation, I begin my work on a new piece of music by taking a collection of basic materials as my starting point. These typically include harmonies, gestures, rhythmic figures, and proportions of form. None of these initial elements are "derived" from other elements within the piece – they are the necessary starting point from which all my other musical ideas will emerge. They give me a place to "hang my hat."
A closer look at constraints
Constraints are self-imposed rules, processes, or practices that can be used as a way of developing, complicating, or expanding our initial axioms or materials. In formal systems developed by human beings, constraints (or inference rules) are either:
- consciously self-imposed
- discovered and derived as "heuristics" based on specific desirable outcomes or goals.
To give an example of this first mode of constraint, I often point to the experimental writer Georges PerecPerec, Georges
Georges Perec was a French author and thinker and a member of the [[Oulipo]] literary group. He is best known for his various books: W, or Memories of Childhood, [[A Void]], and [[Life a User’s Manual]].
Perec's works reflect his interest in constraint techniques, chance, fate, determinism, and memory. See more in the note on the [[Oulipo]].
Resources
James, Alison. Constraining Chance: Georges Perec and the Oulipo. Evanston, IL: Northwestern University Press, 2009.
Last modified on ... who is perhaps best known for his remarkable novel, A VoidCreativity and Constraint- Queering the Formal System
Notes
[[Formal System (Partial) Bibliography]]
I gave a talk entitled Creativity and Constraint – Queering the Formal System to a small virtual gathering of friends in November of 2020. For many years prior, (since about 2012), I had been fascinated by the concept of [[Formal System|formal systems]], where a thinker, writer, musician, mathematician, etc. uses a set of rules to create something new from some initial ideas or "materials."[[Note that this is an extreme simplification of... which he intentionally (and quite miraculously) wrote without using the letter 'e.' (Such literary texts are referred to as lipograms). Perec's ethos and the philosophy of the Oulipo (the literary movement of which Perec was a member) emphasized embracing literary constraints as a path towards the discovery of new ideas, techniques, and ways of thinking. Perec and his fellow writers believed that attempting to severely constrain their typical methods of writing and their natural intuitions would force them into exciting and novel means of creating literary works.
In this spirit, Perec very consciously picked a sort of Mount Everest to scale, constructing a 300-page lipogram in French, intentionally forbidding himself from using the single most common letter of the French alphabet.
While I'm sure that the overall plot, themes, characters, and tenor of the novel were meticulously planned (the precompositional notes to another of Perec's novels, Life a User's Manual, are quite detailed and extensive), I wonder how precisely Perec was able to anticipate the immediate impact of his constraint as he wrote his first draft. It may very well be the case that Perec was familiar with the sorts of permitted lexicons that arise from lipogrammatic constraints on each letter of the French alphabet, but it seems more likely to me that Perec was not primarily interested in the "surface-level" texture that an 'e'-less novel will evoke for the reader. Rather, it appears that the lipogram was primarily a means of making a broader aesthetic/philosophical statement; any letter could do, but 'e' – being the most frequent of French glyphs – would be the most impressive.
Alternatively, some forms of constraints are employed specifically for the nature of the results that they produce. In my compositional work, I use the software OpenMusic to very carefully control the harmonic objects that I derive from my initial materials. This software allows me to program criteria and heuristics that will select for chords and groups of pitches with quite specific properties of consonance, dissonance, homogeneity, etc. I am familiar with these harmonic properties and the sorts of psychological effects that such materials can have on the listener. Unlike the example of A Void above, it will not always do for me to simply swap one harmony for another (like our imagined scenario of Perec choosing a different letter). In this case, I am pursuing a specific sort of result and know the types of tools that I need to use to get there. For an even broader example of this phenomenon in music, interested readers should consult Dimitri Tymoczko's landmark theoretical work, A Geometry of Music. Tymoczko uses statistical analyses of important corpora of Western Classial Music (Bach chorales, Beethoven sonatas, etc.) to derive five heuristics for creating pitch material that listeners will perceive as being tonal. See the Formal System (Partial) Bibliography note for a full citation
Where does this get us?
The last element of our formal system – the result – has some interesting properties of its own. Because the results have been derived from a set collection of axioms/materials and rules/constraints, we often find a wonderful mix of cohesiveness and serendipity.
Mathematicians often remark on the simultaneous beauty and surprise of constructing a proof for this same reason – the rules of mathematical induction that they employ are a way of guaranteeing that each step of the proof is consistent or of-a-piece with what has come before. The whole project of mathematics depends on the idea that we are deriving new statements of truth from old statements of truth.
In my composition work, I use this property of formal systems to ensure that the harmonic materials I used in a piece will all be consistent. Employing a formal system to govern the pitch material of a new work guarantees that the listener will hear a sense of organic developmentOrganicism
The concept of organicism is wily and potentially problematic – it has a history of being a useful aesthetic descriptor, but it can also be attached to a variety of oppressive ideologies. The most salient discussions for my thinking have surrounded organicism in music.
Heinrich Schenker devised influential theories for describing and analyzing works of Western classical music from the "common practice period."[[This time period is from roughly 1650 to 1900.::rsn-transclude]] These theories w... throughout the work.
At the same time, sufficiently complex formal systems can yield surprising results! I often find it difficult if not impossible to ascertain the properties of the results before they have been produced by the application of constraints.
In a similar manner, I understand that mathematicians – even though they are following time-honored practices of mathematical induction – are still surprised when the results of a proof do not match their intuition. The most concisely-stated conjectures of number theory might be the most difficult to solve and the most surprising in their proof or disproof. There are wonderful and strange treasures that formal systems are uniquely adept at discovering.
Finally, it is worth noting that formal systems developed by humans are delightfully prone to little errors and inaccuracies. It is my belief that these "mistakes" are often what truly enrich a work of art or a musical composition – they are moments that provide just enough messiness or surface texture to make the piece seem human or to betray some of the craft behind the concept.
Examples
There are countless examples of formal systems, and I am adding more and more to my list all the time. My personal perspective is that a large proportion of pieces of Western classical music adhere to the concept of the formal system, and so I would include a massive number of pieces in any potential count!
Additionally, I feel that some works are more particularly intentionally in their use of formal systems than others, and so I imagine a sort of gradient or spectrum that describes how rigorously these systems are applied. For example, the very strict forms of canonic imitation that we find in the music of J.S. Bach, Ockeghem, or Taneyev are certainly more rigorously constructed than many other works, such a movement of a work by Liszt. (Note that I do not think that one form of constraint or convention is better than another– Bach and Liszt are attempting to do very different things).
To illustrate some examples of formal systems very quickly, I will rely on excerpts from the work of Georges PerecPerec, Georges
Georges Perec was a French author and thinker and a member of the [[Oulipo]] literary group. He is best known for his various books: W, or Memories of Childhood, [[A Void]], and [[Life a User’s Manual]].
Perec's works reflect his interest in constraint techniques, chance, fate, determinism, and memory. See more in the note on the [[Oulipo]].
Resources
James, Alison. Constraining Chance: Georges Perec and the Oulipo. Evanston, IL: Northwestern University Press, 2009.
Last modified on ... and Anthony Etherin. For an ever-expanding list, see the note Examples of Formal SystemsExamples of Formal Systems
Games
Peter Suber – [[Nomic|Nomic: A Game of Self-Amendment]]
Music[[Of course, I view a large amount of music as following princip....
Excerpt: A Void (Perec)
“It’s on All Saints Day that Anton Vowl would first go missing– as possibly an offshoot of his noticing, just two days prior to this vanishing act, a most alarming story in his Figaro…
Nobody knows, or can know, if his way of quitting this world was wholly of his own volition; nobody in fact knows if Vowl did quit this world at all…
His car was still placidly sitting in its hangar. No stains of blood on floor or wall. No clothing, nor any trunk to carry it in. Missing. Anton Vowl, though, was missing.”
As mentioned aboveCreativity and Constraint- Queering the Formal System
Notes
[[Formal System (Partial) Bibliography]]
I gave a talk entitled Creativity and Constraint – Queering the Formal System to a small virtual gathering of friends in November of 2020. For many years prior, (since about 2012), I had been fascinated by the concept of [[Formal System|formal systems]], where a thinker, writer, musician, mathematician, etc. uses a set of rules to create something new from some initial ideas or "materials."[[Note that this is an extreme simplification of..., Perec writes in A Void without using the letter 'e', and we can see some of the creative solutions he finds (or his English translator Gilbert Adair finds *again*) for navigating this difficulty. Georges Perec, A Void (Boston: Godine, 2005) 37-40.
Instead of referring to Vowl's "disappearance", Adair describes his "vanishing act." Rather than refer to his car in the garage, Adair references its "hangar." In these subtle yet ever-present turns of phrase, Perec and Adar approach language at a slant, bringing to the reader's attention both the mental workings of an author or translator striving against the constraint as well as the multitude of imaginative routes that one may take in describing a single concept.
Example: For Erik Satie (Etherin)
FOR ERIK SATIE (Palindrome-Haiku) Art: Name it, as a
won Gnossienne is song now — a Satie mantra….
In his brief poem, Etherin delightfully imposes two formal constraints, the syllabic count of the haiku (5, 7, and 5 syllables per line) and a palindrome by letter – the letters of the first line are a mirror of the letters of the last. The middle line is mirrored around the 'nn' of Gnossienne (a name for a genre of musical piece that composer Erik Satie invented).
On top of these two constraints is the less obvious but no less difficult challenge of ensuring that the poem make sense. There are any number of poems that can be written as a Palindrome-Haiku that would consist of letters that fail to form words in English. What interests Etherin is the subset of Palindrome-Haikus that will reliably mean something to the intrepid reader.
How is all of this queer?
Thinking about and working with formal systems has helped me to conceptualize my experience of being side B. The three components of formal systems seem to offer tools for answering the following questions:
- What am I working with?
- How do I live my life?
- What can I expect for my future?
Closing Reflections
The side B position itself seems to me to be the result of two almost paradoxical truths: “I’m a Christian with a particular belief about sexual expression,” and “I’m gay.” Through the arduous constraints of theology, deliberation, and lived experience, we create a very messy, beautiful, and compelling piece of art using the logic of our own lives.
Much as a casual observer might wonder why Perec goes to the trouble to write a novel without the letter “e,” we are faced with similar questions from both sides of the culture war: “why do you insist on describing yourself as gay?” or “why don’t you just have sex with the people you like?” Outside observers don’t always realize that when I impose a constraint on my musical ideas or my own existence in the world, I can arrive at a creative freedom which enables discoveries and experiences of the surprising and the sublime. This very community is a testament to both God’s grace in our lives as well as the amazing and resourceful ways that side B people create connection, intimacy, and chosen family in the face of self-imposed constraints.
To be very clear: there is way too much complexity concerning sexuality and the side B experience for the concept of a formal system to adequately encapsulate. Additionally, the creative freedom which self-imposed constraint often encourages does not cancel out the difficulty and heartache of our constraints entirely. Even as we are ingenious and creative and insightful, our lives continue to be difficult in ways that they never should have been. I am not interested in the toxic lieDisambiguation – Constraint vs. Oppression
FREE FROM CONSTRAINT (Sonnet)
Anthony Etherin
I tried to start
again, and shed
the binding thread
that ruled my art.
I let my heart
control my head….
It only bled
and fell apart:
For talent's not
some mystic seed
the soul must find;
instead, its plot
alone is freed
by watchful minds….
One point that I think is important to clarify is the difference between constraint and oppression. Due to the ongoing legacy of the Culture Wars, there are some thinkers who use pretty bad-fait... that artists or LGBT+ people must struggle in order to arrive at fulfillment.
I hope, though, that formal systems will remind us that there is much beauty and freedom and truth to be discovered when we choose a difficult path.
Last modified on 01-28-2022.